A176789 a(n) = (0!! - 1!! + 2!! - 3!! + ... + (-1)^(n-1)*(n-1)!!) mod n.

0, 0, 2, 3, 2, 4, 5, 7, 4, 4, 2, 7, 3, 0, 4, 3, 5, 10, 3, 19, 7, 4, 3, 7, 14, 0, 10, 7, 5, 4, 29, 11, 4, 6, 14, 19, 4, 26, 13, 39, 13, 28, 2, 15, 19, 20, 11, 19, 14, 14, 40, 39, 0, 10, 4, 7, 7, 8, 7, 19, 26, 38, 28, 27, 39, 4, 57, 23, 43, 14, 5, 55, 30, 6, 64, 7, 70, 52, 50, 19, 37, 10, 75, 7

Offset: 1

Author

Paolo P. Lava & Giorgio Balzarotti, Apr 26 2010

Keywords

• easy
• nonn

Comments

Alternating sum of double factorials modulo n.

Examples

			a(1) = 0!! mod 1 = 1 mod 1 = 0.
a(2) = (0!! - 1!!) mod 2 = (1 - 1) mod 2 = 0.
a(3) = (0!! - 1!! + 2!!) mod 3 = (1 - 1 + 2) mod 3 = 2.
		

Crossrefs

Cf. A049782, A176787, A176788.

Programs

Maple

A176789 := proc(n)
        modp(1-(-1)^n*A129831(n-1), n) ;
end proc: # R. J. Mathar, Aug 22 2012

Mathematica

Table[Mod[Sum[(-1)^k k!!,{k,0,n-1}],n],{n,90}] (* Harvey P. Dale, Dec 08 2012 *)

Formula

a(n) = (Sum_{k=0..n-1} (-1)^k*k!!) mod n = (1 + (-1)^(n-1)*A129831(n-1)) mod n.